Question

Find the area of the parallelogram determined by the vectors : 3i + j - 2k and i - 3j + 4k

Answer 1

Given two vectors  \(3\hat i+\hat j-2\hat k\) and  \(\hat i-3\hat j + 4\hat k\)

Let  \(\vec a=3\hat i+\hat j-2\hat k\) and  \(\vec b=\hat i-3\hat j + 4\hat k \)

Recall the area of the parallelogram whose adjacent sides are given by the two vectors  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) and  \(\vec b=b_1\hat i+b_2\hat j+b_3\hat k\) is  \(|\vec a\times\vec b|\) where

Here, we have (a₁, a₂, a₃) = (3, 1, –2) and (b₁, b₂, b₃) = (1, –3, 4)

Recall the magnitude of the vector  \(\text x\hat i+y\hat j + z\hat k\) is

Thus, area of the parallelogram is 10√3 square units.